Step 1: Analyse each statement carefully.
Option (A): Eukaryotic cells possess membrane-bound organelles such as nucleus, mitochondria, endoplasmic reticulum, Golgi apparatus, etc.
\(\Rightarrow\) True
Option (B): Prokaryotic cells do \emph{not} have a true nucleus; their genetic material lies in a nucleoid region.
\(\Rightarrow\) False
Option (C): Although eukaryotic cells do contain genetic information, this statement is too general and not distinguishing, since all living cells (including prokaryotes) possess genetic material.
\(\Rightarrow\) Not the correct choice here.
Option (D): Prokaryotic cells are surrounded by a cell membrane, but this feature is also common to all cells and is not the key distinguishing statement in this question.
\(\Rightarrow\) Not the best answer.
Step 2: Identify the most accurate and distinguishing statement.
The defining and universally accepted true statement among the options is:
\[
\text{Eukaryotic cells have membrane-bound organelles.}
\]
Hence, the correct answer is
\[
\boxed{\text{(A)}}
\]